作业帮已知f(x)=cos^2x+sinxcosx g(x)=2sin(x+π/4)sin(x-π/4)
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已知f(x)=cos^2x+sinxcosx g(x)=2sin(x+π/4)sin(x-π/4)
1、求f（x）的最小正周期及单调增区间
2、若f（a）+g（a）=5/6,且a属于[3π/8,5π/8]
求sin2a的值
尽量这两天，
1、求f（x）的最小正周期及单调增区间
2、若f（a）+g（a）=5/6,且a属于[3π/8,5π/8]
求sin2a的值
尽量这两天，
f(x)=cos^2x+sinxcosx
=(1+cos2x)/2+1/2*sin2x
=1/2+1/2(cos2x+sin2x)
=√2/2*(√2/2*cos2x+√2/2sin2x)+1/2
=√2/2*(sinπ/4cos2x+cosπ/4sin2x)+1/2
=√2/2*sin(π/4+2x)+1/2
T=2π/2=π
2kπ-π/2
=(1+cos2x)/2+1/2*sin2x
=1/2+1/2(cos2x+sin2x)
=√2/2*(√2/2*cos2x+√2/2sin2x)+1/2
=√2/2*(sinπ/4cos2x+cosπ/4sin2x)+1/2
=√2/2*sin(π/4+2x)+1/2
T=2π/2=π
2kπ-π/2
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